\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{0mm}

\usepackage{tkz-fct}
\usetikzlibrary{arrows, decorations.pathreplacing}
\usetikzlibrary{shapes.misc}

\tikzset{
    line/.style={
        very thick,
        black,
        to path={% works only with "to" and not "--"
            -- (\tikztotarget) node[at start,point] {} node [at end,point] {} \tikztonodes
        }
    },
    point/.style={
        ultra thick,
        draw=gray,
        cross out,
        inner sep=0pt,
        minimum width=4pt,
        minimum height=4pt,
    },
}

\begin{document}
\begin{preview}
\begin{tikzpicture}

       \draw[white,fill=white] (-0.5,-0.5) rectangle (7.2,5.2); % background
       \draw[blue!15,fill=blue!15,ultra thick] (1,4) rectangle (6,1); % bounding box
       \draw[red!15,fill=red!15] (1,1) rectangle (4,4); % bounding box
       \tkzInit [xmin=0,xmax=6.5,ymin=0,ymax=4.5]
        \begin{scriptsize}
            \tkzGrid[color = gray!30!white]
            \tkzAxeXY
        \end{scriptsize}

        \draw[line,red] (1,1) to (4,4);

        \draw[line,blue] (1,4) to (6,1);
\end{tikzpicture}
\end{preview}
\end{document}
